The research in this area focuses on the analysis of nonlinear partial differential equations (PDEs) using a wide variety of techniques such as energy and ladder methods, dynamical systems techniques, geometry, and the calculus of variations. The methods are used to analyse PDEs in various contexts such as nonlinear elastostatics, reaction-diffusion systems, dispersive wave equations, Navier-Stokes equations, delay equations, and both dissipative and Hamiltonian equations. Results include advances in regularity theory, estimates for universal attractors, length scales, stability of travelling waves, fronts and solitary waves.